The purpose of this study is to investigate the safety of Lu AF28996, how well it is tolerated and what the body does to the drug in participants with Parkinson's disease.

The study consists of different parts. Part A of the study will consist of once daily (OD) cohorts (OD Cohort 1 to 3), as well as twice daily (BID) cohorts (BID Cohorts A1 and A2). Part B will consist of 3 cohorts (Cohorts B1, B2, and B3) whereby participants will be administered Lu AF28996 BID.

Inclusion Criteria:

• Participants diagnosed with idiopathic PD (consistent with the UK PD Society Brain Bank Criteria for the Diagnosis of PD), with not more than 1 first-degree relative who has PD.
• Participants must have a Modified Hoehn and Yahr score ≤4 in the OFF state and ≤3 in the ON state, and a Mini Mental State Examination score >25.
• The OFF/ON amplitude on the MDS-UPDRS Part III at screening must be minimum 30% difference.
• Participants must experience recognizable and predictable motor fluctuations (with at least 1.5 hours of OFF periods in the awake time, including predictable morning OFF episodes), causing clinically significant disability during the 7-week Screening Period, as evaluated by the investigator. This will be documented using a participant ON/OFF state registration over 3 consecutive days prior to enrolment.
• Allowed concomitant medication for PD during the study includes levodopa, monoamine oxidase B inhibitors, COMT inhibitors, anticholinergics, and amantadine. Dopamine agonists are not allowed and should be discontinued ≥4 weeks prior to dosing with Lu AF28996 and until the end of the study.
• Participants diagnosed with idiopathic PD (consistent with the UK PD Society Brain Bank Criteria for the Diagnosis of PD), with not more than 1 first-degree relative who has PD.
• Participants must have a Modified Hoehn and Yahr score ≥2 to ≤4 in the OFF state and ≤3 in the ON state, a MDS-UPDRS Part IV, 4.5 score of 1 or 2, and a MDS-UPDRS Part IV, 4.2 score ≥2 (at least mild functional impact), and a Mini Mental State Examination score >25 at the Screening Visit.
• Participants must currently have a good response to levodopa and be receiving a stable dose of levodopa (≥3 doses per day of levodopa/dopa decarboxylase inhibitor therapy or ≥3 doses per day of levodopa Extended-Release Capsules and LEDD between 400 and 1600, inclusive) for at least 4 weeks prior to screening.
• Participants must experience recognizable and predictable motor fluctuations (with ≥3 hours of OFF periods in the awake time, including predictable morning OFF episodes), causing clinically significant disability during 3 months prior to enrolment, as evaluated by the investigator. The criteria will be documented using Hauser Diary over 3 consecutive days prior to enrolment.
• Participants must experience ≥1 hour daily ON time with troublesome dyskinesia (TD) in the awake time (TD/24 hours while awake) during the last 3 months prior to enrolment as evaluated by the investigator. The criteria will be documented using the Hauser Diary over 3 consecutive days prior to enrolment.
• Allowed concomitant medication for PD during the study includes levodopa, dopamine agonists, if allowed daily dose, monoamine oxidase B inhibitors, COMT inhibitors, anticholinergics, and amantadine.

Exclusion Criteria:

• The participant has or had one or more of the following conditions that are considered clinically relevant in the context of the study; other neurological disorder, psychiatric disorder, seizure disorder or encephalopathy, respiratory disease, hepatic impairment or renal insufficiency, metabolic disorder, endocrinological disorder, haematological disorder, infectious disorder, any clinically significant immunological condition, or a history of narrow-angle glaucoma.
• Participant has been treated with apomorphine (pen/pump), and/or inhaled levodopa and/or levodopa/carbidopa intestinal gel (LCIG),and/or subcutaneous foslevodopa/foscarbidopa within 6 weeks prior to the Baseline Visit.
• Participants formerly treated with oral or transdermal dopamine agonists must have discontinued 4 weeks prior to screening.
• Participant has a history of Dopamine Agonist Withdrawal Syndrome (DAWS) when dopamine agonists were previously discontinued or reduced.

Other inclusion and exclusion criteria may apply.